Expected Value - Expectation of Matrices

Expectation of Matrices

If X is an m × n matrix, then the expected value of the matrix is defined as the matrix of expected values:

 \operatorname{E} = \operatorname{E} \left [\begin{pmatrix} x_{1,1} & x_{1,2} & \cdots & x_{1,n} \\ x_{2,1} & x_{2,2} & \cdots & x_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ x_{m,1} & x_{m,2} & \cdots & x_{m,n} \end{pmatrix} \right ] = \begin{pmatrix} \operatorname{E} & \operatorname{E} & \cdots & \operatorname{E} \\ \operatorname{E} & \operatorname{E} & \cdots & \operatorname{E} \\ \vdots & \vdots & \ddots & \vdots \\ \operatorname{E} & \operatorname{E} & \cdots & \operatorname{E} \end{pmatrix}.

This is utilized in covariance matrices.

Read more about this topic:  Expected Value

Famous quotes containing the words expectation of and/or expectation:

    In the United States, though power corrupts, the expectation of power paralyzes.
    John Kenneth Galbraith (b. 1908)

    A youthful mind is seldom totally free from ambition; to curb that, is the first step to contentment, since to diminish expectation is to increase enjoyment.
    Frances Burney (1752–1840)